报告题目：Analysis of random evolutions: asymptotic expansions
报告人：Igor Samoilenko, 副教授, 基辅大学
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邀请人：董从造
报告时间：2018年12月25日（周二）下午2:50-3:30
报告地点：信远楼II206数统院报告厅
报告人简介：Igor Samoilenko received M.Sc. degree in mathematics from Kherson State University in 1998. He earned his PhD in 2001 from the Institute of Mathematics of the National Academy of Sciences of Ukraine in Kyiv. In 2014 he received habilitation of PhD degree from Taras Shevchenko National University of Kyiv (KNU), and became an associate Professor in the Department of Computer Science and Cybernetics. Dr. Samoilenko was awarded the Premium of the President of Ukraine for young scientists in 2009. (青年学者总统奖)
Dr. Samoilenko was a scientist and later a senior scientist in the Department of Fractal Analysis of the Institute of Mathematics of the National Academy of Sciences of Ukraine in Kyiv till 2001-2014. He was engaged in research of functional limit theorems for different classes of random evolutions, solution of large deviation problem for processes with independent increments, models of conflict with non-annihilating opponents, etc. He took active part in international projects and has corresponding publications with scientists from University of Bonn (Germany), University of Bielefeld (Germany), Technological University of Compiegne (France).
Dr. Samoilenko’s research interest includes:
(1)Markov and Semi-Markov Processes;
(2)Random Evolutions: Limit Theorems and Asymptotic Expansions;
(3)Large Deviations;
(4)Conflict Models with Non-Annihilating Opponents.
报告摘要：Transport equations are used in mathematical biology to model movement and growth of populations.
Certain bacteria show the following movement pattern: periods of straight runs alternate with periods of random rotations, which leads to re-orientation of the cells. We may model this movement by a velocity jump process, which leads to a transport equation. Random evolutions generalize this model and describe different evolutionary or stochastic systems in random media that is defined by a switching Markov or semi-Markov process.
We study the aforementioned models from two points of view:
(1)Limit theorems that describe their behavior on increasing time intervals; and
(2)Asymptotic expansions of the functionals defined for the pre-limit processes.
The main tool is analysis of the generators of corresponding complex Markov processes or renewal equations in a semi-Markov case.